function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta

J0 = sum(-y.*log(sigmoid(X * theta)) - (1-y).*log(1 - sigmoid(X * theta))) ./ m;
reg = lambda.*sum(theta(2:length(theta)).^2)./(2*m);
J = J0 + reg;

grad0 = X'*(sigmoid(X*theta) - y)./m;
dreg = [0;lambda.*theta(2:length(theta))]./m;
grad = grad0 + dreg;



% =============================================================

end
